fix(pi): close four mode-list gaps in the pi run mode

Review follow-ups on #282. All four are the same failure shape: a list that
enumerates run modes, missed by the sweep that added 'pi'.

1. Cron ignored pi's project-trust clamp. The PR widened CronJobBaseSchema's
   agentType to accept 'pi' but not the matching clamp beside gemini's, so a
   non-granted multi-user owner's cron pi job spawned bare `pi` (pi's own
   defaultProjectTrust, an interactive prompt they can answer "yes" to, which
   loads and EXECUTES repo-local .pi/extensions TypeScript) while the same
   user's UI/API launch was forced to --no-approve. The clamp is now a pure
   exported helper, clampCronExternalCliConfigs(), so both it and gemini's
   previously untested materialization are pinned.

2. POST /api/sessions/:id/interactive auto-enabled the Ralph tracker for pi:
   its denylist covered opencode/codex/gemini/antigravity only. The tracker is
   never fed for an external CLI (_processExpensiveParsers returns early), so a
   pi session reported ralphEnabled and Ralph UI state no sibling backend shows.

3. REMOTE_CLI_BIN had no pi entry, so buildRemoteCliVersionProbeCommand()
   returned null and Session.cliVersion stayed blank for every remote-SSH pi
   session, even though the PR wired the remote launch command and the
   per-mode override schema field.

4. The desktop home rail's badge map had no pi entry, and its lookup falls back
   to '', which is what claude renders. A pi session read as Claude there while
   the tab strip and phone overview badged it correctly.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

src/web/public/home-sessions.js

@@ -69,6 +69,7 @@ const HOME_SESSIONS_MODE_BADGE = {
   codex: 'cx',
   gemini: 'gm',
   antigravity: 'ag',
+  pi: 'pi',
 };
 
 Object.assign(CodemanApp.prototype, {

src/web/routes/session-routes.ts

@@ -1114,12 +1114,16 @@ export function registerSessionRoutes(
 
     try {
       // Auto-detect completion phrase from CLAUDE.md BEFORE starting (only if globally enabled and not explicitly disabled by user)
-      // Ralph tracker is not supported for opencode / codex / gemini / antigravity sessions
+      // Ralph tracker is not supported for opencode / codex / gemini / antigravity / pi sessions.
+      // Keep this list in step with isExternalCliMode(): _processExpensiveParsers() returns early
+      // for those modes, so a tracker enabled here would never be fed, and the session would
+      // still report ralphEnabled + Ralph UI state that no other external CLI shows.
       if (
         session.mode !== 'opencode' &&
         session.mode !== 'codex' &&
         session.mode !== 'gemini' &&
         session.mode !== 'antigravity' &&
+        session.mode !== 'pi' &&
         ctx.store.getConfig().ralphEnabled &&
         !session.ralphTracker.autoEnableDisabled
       ) {